expert's class ahmedabad by dhruv thakar important notes of mathematics class 10 ncert solution also available ,mathematics adda top institute in ahmedabad for mathematics school and And graduation level competitive exam mathematics dhruv sir mobile number-8320495706 ,bhai ka mathematis

1. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
1
Important Questions for Class 10 Maths Chapter 3
Pair of Linear Equations in Two Variables With
Solutions
2016
Short Answer Type Question I [2 Marks]
Question 1.
Solve the following pair of linear equations:
y -4x= 1
6x- 5y= 9
Solution:
Short Answer Type Questions II [3 Marks]
Question 2.
A part of monthly Hostel charge is fixed and the remaining depends on the
number of days one has taken food in the mess. When Swati takes food for
20 days, she has to pay 13000 as hostel charges whereas, Mansi who takes
food for 25 days pays ? 3500 as hostel charges. Find the fixed charges and

2. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
2
the cost of food per day.
Solution:
Question 3.
Solve using cross multiplication method:
x+y=1
2x – 3y = 11
Solution:

3. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
3
Long Answer Type Question [4 Marks]
Question 4.
Draw the graphs of the pair of equations x + 2y = 5 and 2x-3y = – 4. Also find
the points where the lines meet the x-axis.
Solution:

4. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
4
2015
Short Answer Type Question I [2 Marks]

5. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
5
Question 5.
Find whether the lines representing the following pair of linear equations
intersect at a point, are parallel or coincident: 2x – 3y + 6 = 0,4x – 5y + 2 = 0
Solution:
Short Answer Type Questions II [3 Marks]
Question 6.
Given a linear equation 3x-5y = 11. Form another linear equation in these
variables such that the geometric representation of the pair so formed is:
(i) intersecting lines
(ii) coincident lines
(iii) parallel lines
Solution:
Question 7.
Solve for x and y
x + 2y – 3= 0
3x – 2y + 7 = 0
Solution:

6. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
6
Long Answer Type Question [4 Marks]
Question 8.
4 chairs and 3 tables cost ? 2100 and 5 chairs and 2 tables cost ? 1750. Find
the cost of one chair and one table separately
Solution:
2014
Short Answer Type Questions II [3 Marks]
Question 9.
Solve for x andy:
2x= 5y + 4;
3x-2y + 16 = 0
Solution:

7. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
7
Question 10.
Solve for x andy:
Solution:

8. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
8
Question 11.
Solve for x and y:
6(ax + by) = 3a + 2b
6(bx – ay) = 3b -2a
Solution:
Question 12.
Solve the following pair of equations by reducing them to a pair of linear
equations:

9. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
9
Solution:
Question 13.
Determine graphically whether the following pair of linear equations 2x – 3y =
5; 3x + 4y = – 1 has
(i) a unique solution
(ii) infinitely many solutions or
(iii) no solution
Solution:

10. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
10
Question 14.
Find those integral values of m for which the c-coordinate of the point of
intersection of lines represented by y = mx + 1 and 3x + 4y = 9 is an integer.
Solution:
Long Answer Type Questions [4 Marks]

11. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
11
Question 15.
In a two digit number, the digit in the unit place is twice of the digit in the tenth
place. If the digits are reversed, the new number is 27 more than the given
number. Find the number.
Solution:
Question 16.
Solve the following system of linear equations graphically.
3x + y – 12 = 0;
x – 3y + 6 = 0
Shade the region bounded by the lines and ii>axis. Also, find the area of
shaded region.
Solution:

12. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
12
Question 17.
The owner of a taxi company decides to run all the taxi on CNG fuels instead
of petrol/ diesel. The taxi charges in city comprises of fixed charges together
with the charge for the distance covered.
For a journey of 13 km, the charge paid is ? 129 and for journey of 22 km, the
charge paid is ^ 210.
(i) What will a person have to pay for travelling a distance of 32 km?
(ii) Why did he decide to use CNG for his taxi as a fuel?
Solution:
Question 18.
The area of a rectangle reduces by 160 m if its length is increased by 5 m and
breadth is reduced by 4 m. However, if length is decreased by 10 m and
breadth is increased by 2 m, then its area is decreased by 100 m2. Find the
dimensions of the rectangle.

13. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
13
Solution:
Question 19.
At a certain time in a zoo, the number of heads and the number of legs of tiger
and peacocks were counted and it was found that there were 47 heads and
152 legs. Find the number of tigers and peacocks in the zoo:
Why it is necessary to conserve these animals?
Solution:
2013
Short Answer Type Question I [2 Marks]
Question 20.
If the system of equations
6x + 2y = 3 and kx + y = 2 has a unique solution, find the value of k.
Solution:
Short Answer Type Questions II [3 Marks]

14. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
14
Question 21.
Determine the value of m and n so that the following pair of linear equations
have infinite number of solutions.
(2m – l)x + 3y = 5;
3x + (n- l)y = 2
Solution:
Question 22.
For what values of p and q will the following pair of linear equations has
infinitely many solutions?
4x + 5y = 2;
(2p + 7q)x + (p + 8q)y = 2q-p + 1
Solution:
Question 23.
Solve the following pair of equations for x and y

15. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
15
Solution:
Question 24.
8 men and 12 boys can finish a piece of work in 10 days, while 6 men and 8
boys can finish it in 14 days. Find the time taken by one man alone and that
by one boy alone to finish the work.
Solution:
Long Answer Type Questions [4 Marks]
Question 25.
A two digit number is equal to 7 times the sum of its digits. The number
formed by reversing its digits is less than the original number by 18. Find the
original number.

16. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
16
Solution:
Question 26.
The age of the father is twice the sum of the ages of his 2 children. After 20
years, his age will be equal to the sum of the ages of his children. Find the
age of the father.
Solution:
Question 27.
Places A and B are 80 km apart from each other on a highway. A car starts
from A and another from B at the same time. If they move in same direction
they meet in 8 hrs and if they move in opposite directions they meet in 1 hr 20
minutes. Find speeds of the cars.
Solution:

17. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
17
Long Answer Type Questions [4 Marks]
Question 28.
For what value of k will the pair of equations have no solution?
3x + y = 1
(2k-l)x+ (k-l)y = 2k+l
Solution:
Question 29.
Solve for x and y:

18. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
18
Solution:
Question 30.
Solve the following pair of linear equations graphically, x + 3y = 6;2x-3y = 12
Also find the area of the triangle formed by the lines representing the given
equations withy-axis.
Solution:
2011
Short Answer Type Questions I [2 Marks]

19. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
19
Question 31.
Solve: 99x + lOly = 499
lOlx + 99y = 501
Solution:
Question 32.
For what value of p will the following system of equations has no solution;
(2p -1) x + (p -1) y = 2p + 1;
y + 3x – 1 = 0
Solution:
Short Answer Type Questions II [3 Marks]
Question 33.
The sum of the digits of a two digit number is 12. The number obtained by
interchanging the two digits exceeds the given number by 18. Find the
number.

20. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
20
Solution:
Question 34.
In the figure, ABCDE is a pentagon with BE 11 CD and BC 11 DE. BC is
perpendicular to CD. If the perimeter of ABCDE is 21 cm, find the value of x
andy.
Solution:
Question 35.
The sum of the numerator and denominator of a fraction is 12. If 1 is added to
both the numerator and the denominator the fraction becomes 3/4. Find the
fraction.
Solution:

21. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
21
Question 36.
4 men and 6 boys can finish a piece of work in 5 days while 3 men and 4 boys
can finish it in 7 days. Find the time taken by 1 man alone or that by 1 boy
alone.
Solution:
Question 37.
A man travels 600 km partly by train and partly by car. It takes 8 hours and 40
minutes if he travels 320 km by train and the rest by car. It would take 30
minutes more if he travels 200 km by train and the rest by car. Find the speed
of the train and the car separately.
Solution:

22. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
22
Long Answer Type Questions [4 Marks]
Question 38.
Solve the equations graphically:
2x + y = 2;
2y-x = 4
What is the area of the triangle formed by the two lines and the liney = 0?
Solution:
Question 39.
Draw the graphs of the following equations: x + y — 5; x-y = 5
(i) Find the solution of the equations from the graph.
(ii) Shade the triangular region formed by the lines and they-axis.

23. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
23
Solution:
2010
Short Answer Type Questions I [2 Marks]
Question 40.
Find the value of k for which the following pair of linear equations have
infinitely
many solutions : 2x + 3y = 7; (k – l)x + (k + 2)y = 3k
Solution:
Question 41.
Find the value of m for which the pair of linear equations 2x + 3y – 7 = 0 and
(m – l)x + (m + l)y = (3m – 1) has infinitely many solutions.

24. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
24
Solution:
Question 42.
For what value of k will the following pair of linear equations have no solution?
2x + 3y = 9;
6x + (k – 2)y = (3k – 2).
Solution:
Question 43.
For what value of p will the following pair of linear equations have infinitely
many solutions?
(p – 3)x + 3y = p;
px + py = 12
Solution:

25. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
25
Question 44.
Find the values of a and b for which the following pair of linear equations has
infinitely many solutions: 2x + 3y = 7; 3/4(a + b)x + (2a – b)y = 21
Solution:
Question 45.
Solve the following pair of equations:
Solution:
Question 46.
The sum of the numerator and the denominator of a fraction is 4 more than
twice the numerator. If 3 is added to each of the numerator and denominator,
their ratio becomes 2 : 3. Find the fraction. [All India]

26. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
26
Solution:
Question 47.
A number consists of two digits. When the number is divided by the sum of its
digits, the quotient is 7. If 27 is subtracted from the number, the digits
interchange their places, find the number
Solution:
2009
Very Short Answer Type Questions [1 Mark]
Question 48.
Find the value of a so that the point (3, a), lies on the line represented by 2x-

27. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
27
3y = 5
Solution:
Question 49.
Find the number of solutions of the following pair of linear equations .
x + 2y – 8 = 0
2x + 4y = 16
Solution:
Question 50.
Write whether the following pair of linear equations is consistent or not
x +y = 14,
x-y = 4
Solution:
Short Answer Type Questions I [2 Marks]
Question 51.
Find the value of k for which the pair of linear equations
kx + 3y = k – 2 and 12x + ky = k has no solution.
Solution:

28. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
28
Question 52.
Solve for x andy:
Solution:
Question 53.
Without drawing the graph, find out the lines representing the following pair of
linear equations intersect at a point, are parallel or coincident.
Solution:
Question 54.
Solve the following system of equations forx andy
Solution:

29. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
29
Question 55.
Solve the following pair of equations

30. Expert’s class Ahmedabad
By Dhruv Thakar
8320495706
30
Solution: